Relative Free Energies from Non-Equilibrium Simulations: Application to Changes in Density

Abstract

Knowledge of free-energy differences for states of a system provides an essential component in understanding many processes, including solubility, reaction rates, and phase changes. Therefore, the development of efficient, accurate free-energy calculation routines has long been of interest within the field of molecular modelling. Until recently, thermodynamic integration, free-energy perturbation and slow-change techniques were the only approaches available for the calculation of free-energy differences between two states of a system. However, with the discovery of non-equilibrium free-energy relations in the late nineties, new calculation approaches are now possible. This thesis demonstrates the application of these new relations by deriving them from statistical mechanical concepts and applying them to a variety of systems. Although other types of systems are considered, the focus of this work is on the investigation of density changes, as the density of a system is one of its fundamental intrinsic properties, and expansion and compression phenomena are central to many thermodynamic investigations. To investigate the convergence properties of the free-energy calculation methods prior to their application to systems undergoing a density change, a novel transformation between Lennard-Jones systems possessing different potentials is developed and simulations are completed for a variety of transformation parameters. In particular, the accuracy of free-energy calculations as a function of transformation rate is considered, along with a detailed analysis of free-energy convergence as a function of the number of transformations completed.